Sometimes, the electorate moves in mysterious ways. The mayor of Toronto has just admitted that he smoked crack cocaine. That was after months of denying it. As an alibi, he offered the excuse that he was in a drunken stupor. As you might expect, there has been movement in his approval ratings. They have gone in an upward direction.

Most politicians affect not to be bothered by approval ratings. That makes most politicians liars. For a long time, Labour people have not wanted to talk about Ed Miliband's poll numbers. Whenever you raised the subject with his senior aides or members of the shadow cabinet, they would look at their shoes or come up with rather lame explanations or declare that they had to rush away to a meeting. The Labour leader himself would answer questions about his ratings with a shrug of pretended insouciance, burble about "taking the rough with the smooth" and swiftly try to move the conversation on to a different topic.

The reason for this desperate embarrassment was not hard to divine. On most of the qualities that voters look for in a prime minister, Mr Miliband's ratings were dreadful. Try as they might to deny it, he and his strategists knew that this mattered and that it mattered a lot. The Labour leader's inner circle agonised long and frequently about what to do about it and rightly so. No leader of the opposition had had such abysmal ratings and gone on to win power.

Suddenly, things have changed. Labour people are not only willing to talk about their leader's approval ratings, they are quite enthusiastic about discussing them. The reason? They are going up.

I am usually wary when people describe a single event as a "game-changer" and not just because it is such a ghastly cliche. But the Labour leader's speech to his party conference is one of those rare events that seems to qualify for that description. The conference season as a whole does not seem to have made all that much difference to the respective positions of the parties. They have settled back to roughly where they were beforehand. What has changed is Mr Miliband's personal ratings. Among Labour supporters, there has been a transformation – one Tory pollster calls it "dramatic" – from heavily negative to encouragingly positive. Most people, including Mr Miliband, mainly attribute this to the impact of his pledge to freeze energy bills. That is probably right. It provided him with an easy-to-understand signature policy that put flesh on his promise to help "the squeezed middle".

There are clear benefits to the Labour leader from this boost in his ratings. It pumps oxygen into his self-confidence. It earns more respectful attention from the media, ought to improve his authority over his party and causes a flutter of anxiety among his opponents. His strategists believe that if the trend can be sustained it will make it harder for the Tories to chip away at Labour support in critical marginal seats. They also hope that, having engaged the electorate's attention with the energy bill pledge, voters will be more receptive to Labour's broader argument about wages, job creation and spreading prosperity more widely by fashioning a different kind of economy.

This development is prompting some perplexed discussion among Tories. Some of them wonder whether they need to rethink their assumption that they will prevail at the next election by making it a very personal, highly gladiatorial contest, Cameron versus Miliband, which turns the battle on the question of who is fittest to be prime minister. Many Tories, though, remain attached to that as a strategy. They point out that their leader is still a distance ahead when voters are asked: "Who would make best prime minister?" On the performance side of the role, David Cameron remains very accomplished. As one senior Labour figure puts it: "He looks comfortable in the part." He is also relentless about exploiting the opportunities to maximise that advantage. In the words of a very senior Lib Dem: "Cameron milks it. He'll make a sombre statement at the drop of a hat."

The personal ratings of both men are negative: we are in an unusual period when the public doesn't much like any of the candidates on offer. It is not so much a beauty contest as a least-repellent contest. Mr Cameron's advantage is that his overall approval ratings remain less negative, and by some margin, than those of Mr Miliband.

"He fails the 'blink test'," says one Tory strategist, meaning that swing voters still can't imagine the Labour leader standing on the doorstep of Number 10 as prime minister. When this pollster plays clips of the Labour leader to his focus groups, he says: "They can't get past how he looks to listening to what he says." There are three things Mr Miliband could try to do about this. One is cosmetic surgery, which we can rule out. Another would be to admit to smoking crack cocaine, which I would counsel against on the grounds of it being not just illegal but completely unbelievable. The third is to hope that the more people get to know him, the more they will warm to him.

Labour people don't deny that Mr Miliband still has difficulty in coming over as a plausible prime minister. This may be part of the explanation for why about 80% of voters favour the energy price freeze but only half as many think he could actually deliver it. The Labour answer is that he needs to find more ways to attract attention.

One Labour strategist argues: "If people are exposed to two minutes of Ed, they go, 'Oh, it's that weird intellectual with the Marxist dad again. If they are exposed to 20 minutes of him, people go, 'He's much better than we expected. This guy is worth listening to.'" This explains an apparent paradox about the negotiations between the parties about staging TV debates between the leaders during the next election campaign. The talks have stalled. Although it is the Conservatives who say they want the next election to be a presidential one, it is the Tories who are least keen to repeat TV debates. Although it is Labour and the Lib Dems who have the leaders with the poorer personal ratings, they are both enthusiasts for doing it again.

The potential for them to disrupt calculations about elections can be illustrated by two examples from the country that pioneered TV debates. In the 2000 US presidential election, it was widely assumed beforehand that Al Gore, the clever and experienced Democratic vice-president, would have a commanding edge over the Republican challenger from Texas, one George W Bush, a man previously and often derided for his verbal bloopers and lack of knowledge of the world. When Bush turned up for the first debate and delivered a much more fluent and poised performance than many had anticipated, while Gore came over as wooden and remote, expectations were radically changed. Bush went on to win the presidency.

Then there is what happened in the most recent US presidential contest. Before the first TV debate between the candidates, it was widely assumed that Barack Obama, the "great communicator", would best Mitt Romney. As it turned out, the Republican performed above expectations and the president flopped. In a compelling new book about that contest, Double Down, Mark Halperin and John Heilemann quote Obama's strategist, David Plouffe. "If we don't fix this," he tells the team, "we could lose the whole fucking election." In the end, Obama raised his game and went on to victory, but it highlights how debates can upset assumptions and calculations.

Labour wants TV debates at the next election in the belief that Ed Miliband will exceed expectations and benefit from the prolonged exposure he would receive. They would have the added advantage, so believe Labour people, of giving him a platform to address the country directly rather than have his messages "mediated and distorted by the rightwing press". The Lib Dems are just as keen on more TV debates. They gave Nick Clegg his great opportunity to shine last time. To this day, many Tories believe that gifting equal status to the Lib Dem leader cost the Conservatives a parliamentary majority. Mr Clegg is hardly going to be able to present himself as the clean-handed candidate of change unsullied by power. One of his greatest worries about the next election is that his party will be "squeezed" if the argument is reduced to a battle about who should be prime minister. TV debates at the next election are vital, in the view of the Lib Dem leader, to resist being marginalised.

It is the Tories who are proving most difficult about agreeing to more TV debates. One Labour figure familiar with the negotiations says they are paralysed because the Tories "are playing silly buggers". Lib Dems confirm this and say they suspect the Conservatives would rather return to "an old-fashioned type of campaign" dominated by leaders' tours and morning news conferences. Last time around, Mr Clegg threw Tory calculations into chaos by performing much better than they had anticipated. They don't want to be surprised again by finding that Mr Miliband comes over better in debates than they had expected. The dilemma for the Conservatives is whether it would be even riskier for David Cameron to look as if he is frit.